Interplay of Chemical Disorder, Vortex Pinning, and Electron Correlations in the Mechanically Robust Medium-Entropy Alloy Superconductor $\text{Nb}_{0.45}\text{Ta}_{0.25}\text{Ti}_{0.15}\text{Hf}_{0.15}$

Medium and high-entropy alloys have emerged as a promising class of superconducting materials because their intrinsic chemical disorder can simultaneously enhance mechanical robustness and modify superconducting properties. Here, we present a combined experimental and first-principles investigation of the structural, superconducting, electronic, and local lattice-distortion characteristics of the mechanically robust medium-entropy alloy $\text{Nb}_{0.45}\text{Ta}_{0.25}\text{Ti}_{0.15}\text{Hf}_{0.15}$. The material shows type-II superconductivity with a transition temperature $T_C^{onset} \approx 7.8 ~\mathrm{K}$. A high critical current density of $J_c = 0.48 \times 10^{6}~\mathrm{A/cm^2}$ is observed, and this is attributed to strong vortex pinning at grain boundaries. Specific-heat analysis indicates a strong electron-phonon coupling ($λ$ = 1.07) with a large isotropic s-wave superconducting gap. Density functional theory calculations explicitly model the intrinsic chemical disorder, predict a stable body-centered cubic phase. These calculations further reveal a metallic electronic structure with substantial Ti- and Ta-derived states at the Fermi level. Additionally, our results quantify a pronounced disorder-induced local lattice distortion ($Δd = 0.086$ A), providing a microscopic basis for the experimentally observed enhanced vortex-pinning landscape. Remarkably, the alloy also exhibits an unusually large Kadowaki-Woods ratio, placing it close to the heavy-fermion regime and indicating enhanced electronic correlations beyond conventional alloy superconductors. Our results demonstrate that entropy-engineered chemical disorder can stabilize robust superconductivity, promote strong flux pinning, and induce correlated electronic behavior, establishing refractory medium-entropy alloys as a promising platform for next-generation superconducting materials.